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On 18 August 1913, at the Monte Carlo casino, one roulette wheel made history: black came up twenty-six times in a row. By the fifteenth spin, the table was frenzied: gamblers piled ever-bigger bets on red, convinced it was 'due'. The casino made millions of francs that night.
The reasoning feels like common sense and is pure illusion: the ball has no memory. On every spin, black and red have the same odds as the spin before. Such a streak is astonishingly rare, on the order of one in tens of millions, but after twenty-five blacks, the next is as likely as ever.
The mistake has a name: the gambler's fallacy, or Monte Carlo fallacy. It isn't confined to casinos: it shows up when you think a lottery number is 'overdue', that a coin 'owes' you heads, or that a stock 'has to bounce back' after five falling days.
Chance keeps no accounts and owes you nothing. Every spin starts from zero; the streak exists only in your head.